1. REVIEW & PRACTICE for the Test

2. Volume is the number of cubic units needed to fill a space.

3. It takes 10, or 5 · 2, centimeter cubes to cover the bottom layer of this rectangular prism.
There are 3 layers of 10 cubes each. It takes 30, or 5 · 2 · 3, cubes to fill the prism.
The volume of the prism is 5 cm · 2 cm · 3 cm = 30 cm3.

4. Additional Example 1: Finding the Volume of a Rectangular Prism
Find the volume of the rectangular prism.
13 in.
11 in.
26 in.
V = lwh
Write the formula.
V = 26 • 11 • 13
l = 26; w = 11; h = 13
V = 3,718 in3
Multiply.

5. Try This: Example 1
Find the volume of the rectangular prism.
16 in.
12 in.
29 in.
V = lwh
Write the formula.
V = 29 • 12 • 16
l = 29; w = 12; h = 16
V = 5,568 in3
Multiply.

6. To find the volume of any prism, you can use the formula V= Bh, where B is the area of the base, and h is the prism’s height. So, to find the volume of a triangular prism, B is the area of the triangular base and h is the height of the prism.

7. Additional Example 2A: Finding the Volume of a Triangular Prism
Find the volume of each triangular prism. A.
V = Bh
Write the formula.
V = ( • 3.9 • 1.3) • 4 1 2 __
B = • 3.9 • 1.3; h = 4. 1 2 __
V = m3
Multiply.

8. Additional Example 2B: Finding the Volume of a Triangular Prism
Find the volume of the triangular prism. B.
V = Bh
Write the formula.
V = ( • 6.5 • 7) • 6 1 2 __
B = • 6.5 • 7; h = 6. 1 2 __
V = ft 3
Multiply.

9. Try This: Example 2A
Find the volume of each triangular prism. A.
7 m
1.6 m
4.2 m
V = Bh
Write the formula.
V = ( • 4.2 • 1.6) • 7 1 2 __
B = • 4.2 • 1.6; h = 7. 1 2 __
V = m3
Multiply.

10. Try This: Example 2B
Find the volume of each triangular prism. B.
9 ft
5 ft
4.5 ft
V = Bh
Write the formula.
V = ( • 4.5 • 9) • 5 1 2 __
B = • 4.5 • 9; h = 5. 1 2 __
V = ft3
Multiply.

11. Learn to find volumes of cylinders.

12. To find the volume of a cylinder, you can use the same method as you did for prisms: Multiply the area of the base by the height.
volume of a cylinder = area of base  height
The area of the circular base is r2, so the formula is V = Bh = r2h.

13. Additional Example 1A: Finding the Volume of a Cylinder
Find the volume V of the cylinder to the nearest cubic unit. A.
V = r2h
Write the formula.
V  3.14  42  7
Replace  with 3.14, r with 4, and h with 7.
V 
Multiply.
The volume is about 352 ft3.

14. Additional Example 1B: Finding the Volume of a Cylinder
10 cm ÷ 2 = 5 cm
Find the radius.
V = r2h
Write the formula.
V  3.14  52  11
Replace  with 3.14, r with 5, and h with 11.
V  863.5
Multiply.
The volume is about 864 cm3.

15. Additional Example 1C: Finding the Volume of a Cylinder3 __
Find the radius.
r = = 7 9 3 __
Substitute 9 for h.
V = r2h
Write the formula.
V  3.14  72  9
Replace  with 3.14, r with 7, and h with 9.
V  1,384.74
Multiply.
The volume is about 1,385 in3.

16. What is a Right Triangle?
The Pythagorean Theorem applies only to right triangles.
A right triangle is a triangle that has a 90 degree right angle. It has two legs and a hypotenuse.
The hypotenuse is the side opposite the right angle and is always the longest.
The variables a + b are used for the legs and c is the variable for the hypotenuse. a c b